Simulation Periods

Amolecular dynamics simulation can have three distinct time and temperature periods heating, simulation (run), and cooling. If you want to measure equilibrium properties of a molecular system, you can divide the simulation period into two parts equilibration and data collection. 

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Computer simulations of bulk liquids are usually performed by employing periodic boundary conditions in all three directions of space, in order to eliminate artificial surface effects due to the small number of molecules. Most simulations of interfaces employ parallel planar interfaces. In such simulations, periodic boundary conditions in three dimensions can still be used. The two phases of interest occupy different parts of the simulation cell and two equivalent interfaces are formed. The simulation cell consists of an infinite stack of alternating phases. Care needs to be taken that the two phases are thick enough to allow the neglect of interaction between an interface and its images. An alternative is to use periodic boundary conditions in two dimensions only. The first approach allows the use of readily available programs for three-dimensional lattice sums if, for typical systems, the distance between equivalent interfaces is at least equal to three to five times the width of the cell parallel to the interfaces. The second approach prevents possible interactions between interfaces and their periodic images. 

Figure 14 The predicted uptake of phosphorus by maize over a 22 day period. The Barber-Cushman model (F, ), u.ses an average root radius calculated at the end of the simulation period, while the F, model uses a population of roots of different radius. Identical parameter values were used by both simulation models with the exception of root radius.

Modeling Numerical modeling was conducted using HYDRUS 2-D, which simulated the wettest year on record over the simulation period of 10 years. The model predicted approximately 0.6 mm of percolation during the first year, and 0.1 mm per year for the remaining... 

A global sensitivity analysis was performed for the lead concentration in the arterial blood model (Fig. 7) over the simulation period for each parameter. Parameters considered for the sensitivity analysis are listed in Table 8 (Annex 1). The magnitude of sensitivity is shown by relative sensitivity index. It was observed that the most influential parameter is the porosity of the sediment of the river (phi sed)... 

Fig. 2.3 I nventory, Backlog, and Transit Quantity during simulated period.

FIGURE 1.21 Trajectories of the intermolecular energies for (a) the strong -complex and (b) the weak / -complex between 0-9-(r rr-butylcarbamoyl)-6 -neopentoxy-cinchonidine and DNB-Leu over the 1 ns simulation period in the polar (water) medium. (Top) Coulomb energy (middle) Van der Waals energy (bottom) total energy. (Reprinted from N.M. Maier et al., J. Am. Chem. Soc., 124 8611 (2002). With permission.)... 

The formation of MSA is a function of the OH concentration. Despite mean OH levels over the whole simulation period in "polluted" air exceeding those in "clean" air, predicted MSA concentrations at the inland site do not in general, reflect these differences. The explanation lies in the amount of DMS oxidation by NO3 that has occurred over the North Sea. If darkness, and correspondingly increased NO, levels, occur closer to Scandinavia than the UK,... 

The conformational behavior of Aim inserted in a POPC bilayer has been investigated using the same system as described above [87]. To insert the Aim molecule, a hole was introduced by restraints and one POPC molecule was removed. The Aim was placed into the bilayer, the system was hydrated, and one sodium ion added. A second simulation was performed in which no sodium ion was added and Glu18 was protonated instead. During the simulation period of 1000 ps, the Aim molecule remained in its a-helical conformation, showing only small fluctuations in the root mean square distance (RMSD) of the Ca atoms underlining its conformational stabilization by the lipid bilayer. 

The all-trcms conformation of both guest molecules was maintained throughout the simulation period, but the molecular axis jumped several times between three symmetry-related sites this corresponds to a rate of 1010-1012 s-1. 

The following is often used. We choose exponentially increasing time intervals over some period r, which may be the total simulation period, a pulse duration or (see below) a single whole time interval to be subdivided. The period is divided into Al intervals of length 8tk, k 1,AI. Assume the... 

CN is formally as stable as Laasonen, and more accurate, with errors of 0(STA, Ha). However, it has one serious drawback. If the initial conditions are a sharp change in concentration (as in potential jump experiments), CN responds with errors oscillating about zero and for large A values these oscillations can persist over much of the simulation period. This has meant that simulators have tended to use other methods instead. The stability, and the reason for the oscillatory response, of CN are explained in Chap. 14, but here, a method of damping the oscillations will be described. 

Fig. 6. Visulization of the Monte Carlo simulation periodic boundary conditions are used where the mirror image of a particle enters through the opposite face when a particle leaves (Ref. 24).

To avoid potential water-vacuum interface problems that might arise in a MD simulation, periodic boundary conditions arc commonly used." Basically, a protein is surrounded by a rectangular hox of water with a defined number of water structures. This water box is then surrounded un each face by another water box. When the MD simulation is being carried out. water near the edges of the central box containing the protein may leave and be replaced with a water coming from the water box on the opposite side. This procedure ensures that the waters inside the central water box remain constant. 

When we solve the problem numerically, the number of surface elements, and consequently, the size of the dielectric boundary surfaces must be finite. This is in accordance with the practice in a simulation, where the simulation cell is also finite. To approximate an infinite system in a simulation, periodic boundary conditions are applied in the x and y directions. The closest image convention is used not only for the ionic distances but any distances between... 

Calculations were started with initial concentrations as shown in Table 4. Initial concentrations of all further compounds were set to zero. Results of the calculations are shown in Figure 1. We present numbers obtained after a simulation period of 100 min with constant reaction rates. Although concentrations of the stable compounds H2O2, NOs, HCHO, and ORG steadily decrease due to the photolysis reactions or the reactions with OH, calculated concentrations remain relatively constant over longer periods. For example, concentrations of the stable compounds changed less than 1% after the simulation of 100 min (Figure 1) compared to the initial concentrations (Table 4). 

Figure 1 Sources and sinks of OH calculatedfor the QLL of surface snoM Numbers are calculated after a simulation period of 100 minutes. Numbers in brackets refer to reactions as shown in Table 2.

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